Question

A chord of a circle is equal to the radius of the circle. find the angle subtended by the chord at a point on the major arc.

Answer 1

it forms an equilateral triangle.
so angle subtended by arc at the centre is doubled the angle subtended on any part of the circle
so 60/2=30°

Answer 2

Hi

Here devil1407,

In ΔOAB,

AB = OA = OB (radii)
                    Hence ΔOAB is an equilateral triangle
    That is each angle of ΔOAB is 60°
∴ ∠AOB = 60°

∠AOB = 2∠ACB [Angle subtended by an arc of a circle at the centre is double the angle subtended by it on any part of the circle]
          Hence ∠ACB = 30°
In cyclic quadrilateral ADBC
∠ADB + ∠ACB = 180° (Sum of opposite angles in a cyclic quadrilateral is 180°)
    ⇒ ∠ADB = 180° − 30° = 150°

Therefore, the angle subtended by the chord at a point on the major arc and the minor arc is 30° and 150° respectively.

Hope it helps U

Bye